Unified Framework of Woodin Cardinal as a Holographic Renormalization Group Invariant

This paper establishes a unified framework for Woodin cardinal κ as a fundamental physical invariant in quantum gravity unification. We syn thesize three breakthrough perspectives: (1) κ as a renormalization group invariant derived from AdS/CFT correspondence, (2) rigorous error con trol via enhanced TOENS framework with tensor norm constraints, and (3) experimental signatures including gravitational wave spectral dips, quantum error correction thresholds, and CMB polarization modifica tions. The unified expression κ = K R g gUV IR dg/p β(g) resolves critical con troversies in quantum gravity. Verification pathways span LISA (2034), quantum processors (2027), and LiteBIRD (2027), establishing quantum gravity as an experimental discipline. Key enhancement: We resolve the apparent tension between Woodin cardinal’s infinitary nature and physical constant’s finiteness through Ji uzhang Constructive Mathematics, implementing domain confinement, operational finitization, and dual isomorphism.